Symmetry and monotonicity results for positive solutions of p-Laplace systems

TL;DR

This paper extends symmetry and monotonicity results for positive solutions from scalar p-Laplace equations to systems involving p-Laplacians, using the moving hyperplanes method under certain conditions.

Contribution

It introduces new symmetry and monotonicity results for p-Laplace systems, generalizing previous scalar case findings using advanced mathematical techniques.

Findings

Extended symmetry results to p-Laplace systems

Applied moving hyperplanes method to systems

Established conditions for monotonicity and symmetry

Abstract

We extend to the case of a system involving p-Laplacians, the monotonicity and symmetry results of Damascelli and Pacella obtained in the case of a scalar p-Laplace equation with $1<p<2$. For this purpose, we use the moving hyperplanes method and we suppose that the right hand sides are increasing and locally Lipschitz continuous.